Fermi-Pasta-Ulam recurrences of incoherent waves

In the early 1950s, Fermi, Pasta and Ulam (FPU) published a seminal report in which they numerically investigated the dynamics of a one-dimensional anharmonic chains of particles. They argued that, owing to the nonlinear coupling, the system would irreversibly relax to a state of thermal equilibrium, in which the energy is equidistributed among all modes. Instead of such a thermalization process, FPU observed a recurrent transfer of energy among only few neighbouring modes. Such an energy transfer is reversible since after some time the system nearly goes back to its initial state. The attempt to resolve the paradox of FPU recurrences had a deep impact in the development of nonlinear science, such as the discovery of integrability and solitons.